Dirichlet character χ2600(1217,⋅)\chi_{2600}(1217,\cdot)

• Label: 2600.1217
• Modulus: $2600$
• Conductor: $325$
• Order: $20$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2600$
Conductor:	$325$
Order:	$20$
Real:	no
Primitive:	no, induced from $\chi_{325}(242,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 2600.em

$\chi_{2600}(177,\cdot)$ $\chi_{2600}(473,\cdot)$ $\chi_{2600}(697,\cdot)$ $\chi_{2600}(1217,\cdot)$ $\chi_{2600}(1513,\cdot)$ $\chi_{2600}(1737,\cdot)$ $\chi_{2600}(2033,\cdot)$ $\chi_{2600}(2553,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	20.20.148970555205860748537816107273101806640625.1

Values on generators

$(1951,1301,1977,1601)$ → $(1,1,e\left(\frac{13}{20}\right),i)$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 2600 }(1217, a)$	$1$	$1$	$e\left(\frac{11}{20}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$